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A247458 Numbers k such that d(r,k) = 1 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {3*sqrt(2)}, and { } = fractional part. 4
3, 5, 7, 13, 16, 17, 19, 23, 27, 30, 31, 32, 33, 34, 36, 39, 40, 43, 44, 46, 50, 53, 56, 61, 68, 73, 74, 75, 76, 80, 84, 87, 91, 94, 97, 99, 101, 103, 105, 114, 115, 116, 118, 120, 123, 124, 125, 127, 131, 132, 137, 140, 141, 142, 146, 154, 156, 158, 160 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every positive integer lies in exactly one of these: A247455, A247456, A247457, A247458.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

EXAMPLE

{1*sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1,...

{3*sqrt(2)} has binary digits 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1,...

so that a(1) = 3 and a(2) = 5.

MATHEMATICA

z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[3*Sqrt[2]];

u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]]

v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]]

t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];

t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];

t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];

t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];

Flatten[Position[t1, 1]]  (* A247455 *)

Flatten[Position[t2, 1]]  (* A247456 *)

Flatten[Position[t3, 1]]  (* A247457 *)

Flatten[Position[t4, 1]]  (* A247458 *)

CROSSREFS

Cf. A247455, A247456, A247457.

Sequence in context: A192110 A246026 A188574 * A008996 A261089 A264988

Adjacent sequences:  A247455 A247456 A247457 * A247459 A247460 A247461

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 18 2014

STATUS

approved

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Last modified January 17 20:36 EST 2020. Contains 330987 sequences. (Running on oeis4.)